Start with the basic function f (x) = 2x. If you have an initial value of 1, then you end up with the
following iterations.
· f(1)= 2 *1 =2
· f2(1) = 2 * 2 * 1 = 4
· f3(1)= 2 * 2 * 2 * 1 = 8
Questions
1. If you continue this pattern, what do you expect would happen to the numbers as the
number of iterations grows? Check your result by conducting at least 10 iterations.
2. Repeat the process with an initial value of -1. What happens as the number of
iterations grows?
1. As the number of iterations grows, the numbers will continue to double each time.
· f4(1) = 2 * 2 * 2 * 2 * 1 = 16
· f5(1) = 2 * 2 * 2 * 2 * 2 * 1 = 32
· f6(1) = 2 * 2 * 2 * 2 * 2 * 2 * 1 = 64
· f7(1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1 = 128
· f8(1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1 = 256
· f9(1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1 = 512
· f10(1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 1 = 1024
2. With an initial value of -1, the numbers will continue to alternate between negative and positive values, doubling in magnitude each time.
· f(-1) = 2 * (-1) = -2
· f2(-1) = 2 * 2 * (-1) = 4
· f3(-1) = 2 * 2 * 2 * (-1) = -8
· f4(-1) = 2 * 2 * 2 * 2 * (-1) = 16
· f5(-1) = 2 * 2 * 2 * 2 * 2 * (-1) = -32
· f6(-1) = 2 * 2 * 2 * 2 * 2 * 2 * (-1) = 64
· f7(-1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * (-1) = -128
· f8(-1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * (-1) = 256
· f9(-1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * (-1) = -512
· f10(-1) = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * (-1) = 1024